Such balancing or measuring adapters are used for clamping a rotating component onto a balancing or measuring machine. A balancing machine having a balancing adapter of the type in question is known from DE 299 80 181. It contains a main body having a centered receiving opening for the component to be clamped and a claw actuating unit, movable relative to the main body, for a collet chuck. In this known design, the collet chuck is fixedly mounted on the main body and is not movable axially relative thereto. The clamping tongues of the collet chuck are therefore moved only radially when the claw actuating unit is displaced axially, and therefore the axial retraction travel is limited.